CGAL 4.11  Polygon Mesh Processing

Functions to triangulate faces, and to refine and fair regions of a polygon mesh.
Functions  
template<typename VertexRange , typename TriangleMesh , typename NamedParameters >  
void  CGAL::Polygon_mesh_processing::random_perturbation (VertexRange vertices, TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np) 
randomly perturbs the locations of vertices of a triangulated surface mesh. More...  
template<typename TriangleMesh , typename NamedParameters >  
void  CGAL::Polygon_mesh_processing::random_perturbation (TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np) 
same as above, but all nonborder vertices of tmesh are perturbed.  
template<typename TriangleMesh , typename FaceRange , typename FaceOutputIterator , typename VertexOutputIterator , typename NamedParameters >  
std::pair< FaceOutputIterator, VertexOutputIterator >  CGAL::Polygon_mesh_processing::refine (TriangleMesh &tmesh, const FaceRange &faces, FaceOutputIterator faces_out, VertexOutputIterator vertices_out, const NamedParameters &np) 
refines a region of a triangle mesh More...  
template<typename TriangleMesh , typename VertexRange , typename NamedParameters >  
bool  CGAL::Polygon_mesh_processing::fair (TriangleMesh &tmesh, const VertexRange &vertices, const NamedParameters &np) 
fairs a region on a triangle mesh. More...  
template<typename PolygonMesh , typename FaceRange , typename NamedParameters >  
void  CGAL::Polygon_mesh_processing::isotropic_remeshing (const FaceRange &faces, const double &target_edge_length, PolygonMesh &pmesh, const NamedParameters &np) 
remeshes a triangulated region of a polygon mesh. More...  
template<typename PolygonMesh , typename EdgeRange , typename NamedParameters >  
void  CGAL::Polygon_mesh_processing::split_long_edges (const EdgeRange &edges, const double &max_length, PolygonMesh &pmesh, const NamedParameters &np) 
splits the edges listed in edges into subedges that are not longer than the given threshold max_length . More...  
template<typename PolygonMesh , typename NamedParameters >  
bool  CGAL::Polygon_mesh_processing::triangulate_face (typename boost::graph_traits< PolygonMesh >::face_descriptor f, PolygonMesh &pmesh, const NamedParameters &np) 
triangulates a single face of a polygon mesh. More...  
template<typename FaceRange , typename PolygonMesh , typename NamedParameters >  
bool  CGAL::Polygon_mesh_processing::triangulate_faces (FaceRange face_range, PolygonMesh &pmesh, const NamedParameters &np) 
triangulates given faces of a polygon mesh. More...  
template<typename PolygonMesh , typename NamedParameters >  
bool  CGAL::Polygon_mesh_processing::triangulate_faces (PolygonMesh &pmesh, const NamedParameters &np) 
triangulates all faces of a polygon mesh. More...  
bool CGAL::Polygon_mesh_processing::fair  (  TriangleMesh &  tmesh, 
const VertexRange &  vertices,  
const NamedParameters &  np  
) 
fairs a region on a triangle mesh.
The points of the selected vertices are relocated to yield an assmoothaspossible surface patch, based on solving a linear biLaplacian system with boundary constraints, described in [3]. The optional parameter fairing_continuity
gives the ability to control the tangential continuity C^{ n} of the output mesh.
The region described by vertices
might contain multiple disconnected components. Note that the mesh connectivity is not altered in any way, only vertex locations get updated.
Fairing might fail if fixed vertices, which are used as boundary conditions, do not suffice to solve constructed linear system.
Note that if the vertex range to which fairing is applied contains all the vertices of the triangle mesh, fairing does not fail, but the mesh gets shrinked to CGAL::ORIGIN
.
TriangleMesh  a model of FaceGraph and MutableFaceGraph 
VertexRange  a range of vertex descriptors of TriangleMesh , model of Range . Its iterator type is InputIterator . 
NamedParameters  a sequence of Named Parameters 
tmesh  the triangle mesh with patches to be faired 
vertices  the vertices of the patches to be faired (the positions of only those vertices will be changed) 
np  optional sequence of Named Parameters among the ones listed below 
vertex_point_map  the property map with the points associated to the vertices of tmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in TriangleMesh 
fairing_continuity  tangential continuity of the output surface patch. The larger fairing_continuity gets, the more fixed vertices are required 
sparse_linear_solver  an instance of the sparse linear solver used for fairing 
true
if fairing is successful, otherwise no vertices are relocatedis_triangle_mesh(tmesh)
#include <CGAL/Polygon_mesh_processing/fair.h>
void CGAL::Polygon_mesh_processing::isotropic_remeshing  (  const FaceRange &  faces, 
const double &  target_edge_length,  
PolygonMesh &  pmesh,  
const NamedParameters &  np  
) 
remeshes a triangulated region of a polygon mesh.
This operation sequentially performs edge splits, edge collapses, edge flips, tangential relaxation and projection to the initial surface to generate a smooth mesh with a prescribed edge length.
PolygonMesh  model of MutableFaceGraph . The descriptor types boost::graph_traits<PolygonMesh>::face_descriptor and boost::graph_traits<PolygonMesh>::halfedge_descriptor must be models of Hashable . If PolygonMesh has an internal property map for CGAL::face_index_t , and no face_index_map is given as a named parameter, then the internal one must be initialized 
FaceRange  range of boost::graph_traits<PolygonMesh>::face_descriptor , model of Range . Its iterator type is ForwardIterator . 
NamedParameters  a sequence of Named Parameters 
pmesh  a polygon mesh with triangulated surface patches to be remeshed 
faces  the range of triangular faces defining one or several surface patches to be remeshed 
target_edge_length  the edge length that is targeted in the remeshed patch. If 0 is passed then only the edgeflip, tangential relaxation, and projection steps will be done. 
np  optional sequence of Named Parameters among the ones listed below 
target_edge_length
geom_traits  a geometric traits class instance, model of Kernel . Exact constructions kernels are not supported by this function. 
vertex_point_map  the property map with the points associated to the vertices of pmesh . Instance of a class model of ReadWritePropertyMap . 
face_index_map  a property map containing the index of each face of pmesh 
number_of_iterations  the number of iterations for the sequence of atomic operations performed (listed in the above description) 
edge_is_constrained_map  a property map containing the constrainedornot status of each edge of pmesh . A constrained edge can be split or collapsed, but not flipped, nor its endpoints moved by smoothing. Note that patch boundary edges (i.e. incident to only one face in the range) are always considered as constrained edges. 
vertex_is_constrained_map  a property map containing the constrainedornot status of each vertex of pmesh . A constrained vertex cannot be modified at all during remeshing 
protect_constraints  If true , the edges set as constrained in edge_is_constrained_map (or by default the boundary edges) are not split nor collapsed during remeshing. Note that around constrained edges that have their length higher than twice target_edge_length , remeshing will fail to provide good quality results. It can even fail to terminate because of cascading vertex insertions. 
face_patch_map  a property map with the patch id's associated to the faces of faces . Instance of a class model of ReadWritePropertyMap . It gets updated during the remeshing process while new faces are created. 
number_of_relaxation_steps  the number of iterations of tangential relaxation that are performed at each iteration of the remeshing process 
relax_constraints  If true , the end vertices of the edges set as constrained in edge_is_constrained_map and boundary edges move along the constrained polylines they belong to. 
split_long_edges()
add possibility to provide a functor that projects to a prescribed surface
Deal with exact constructions Kernel. The only thing that makes sense is to guarantee that the output vertices are exactly on the input surface. To do so, we can do every construction in double
, and use an exact process for projection. For each vertex, the AABB_tree
would be used in an inexact manner to find the triangle on which projection has to be done. Then, use CGAL::intersection(triangle, line)
in the exact constructions kernel to get a point which is exactly on the surface.
#include <CGAL/Polygon_mesh_processing/remesh.h>
void CGAL::Polygon_mesh_processing::random_perturbation  (  VertexRange  vertices, 
TriangleMesh &  tmesh,  
const double &  perturbation_max_size,  
const NamedParameters &  np  
) 
randomly perturbs the locations of vertices of a triangulated surface mesh.
By default, the vertices are reprojected onto the input surface after perturbation. Note that no geometric checks are done after the perturbation (face orientation might become incorrect and selfintersections might be introduced).
VertexRange  model of Range , holding vertices of type boost::graph_traits<TriangleMesh>::vertex_descriptor . Its iterator type is ForwardIterator . 
TriangleMesh  model of MutableFaceGraph . 
NamedParameters  a sequence of Named Parameters 
vertices  the range of vertices to be perturbed 
tmesh  the triangulated surface mesh 
perturbation_max_size  the maximal length of moves that can be applied to vertices of tmesh . 
np  optional sequence of Named Parameters among the ones listed below 
geom_traits  a geometric traits class instance, model of Kernel . 
vertex_point_map  the property map with the points associated to the vertices of tmesh . Instance of a class model of ReadWritePropertyMap . 
vertex_is_constrained_map  a property map containing the constrainedornot status of each vertex of tmesh . A constrained vertex cannot be modified at all during perturbation 
do_project  a boolean that sets whether vertices should be reprojected on the input surface after their coordinates random perturbation 
random_seed  a nonnegative integer value to seed the random number generator, and make the perturbation deterministic 
#include <CGAL/Polygon_mesh_processing/random_perturbation.h>
std::pair<FaceOutputIterator, VertexOutputIterator> CGAL::Polygon_mesh_processing::refine  (  TriangleMesh &  tmesh, 
const FaceRange &  faces,  
FaceOutputIterator  faces_out,  
VertexOutputIterator  vertices_out,  
const NamedParameters &  np  
) 
refines a region of a triangle mesh
TriangleMesh  model of MutableFaceGraph 
FaceRange  range of face descriptors, model of Range . Its iterator type is InputIterator . 
FaceOutputIterator  model of OutputIterator holding boost::graph_traits<TriangleMesh>::face_descriptor for patch faces 
VertexOutputIterator  model of OutputIterator holding boost::graph_traits<TriangleMesh>::vertex_descriptor for patch vertices 
NamedParameters  a sequence of Named Parameters 
tmesh  triangle mesh with patches to be refined 
faces  the range of faces defining the patches to refine 
faces_out  output iterator into which descriptors of new faces are recorded 
vertices_out  output iterator into which descriptors of new vertices are recorded 
np  optional sequence of Named Parameters among the ones listed below 
vertex_point_map  the property map with the points associated to the vertices of tmesh Instance of a class model of ReadWritePropertyMap . If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in TriangleMesh 
density_control_factor  factor to control density of the output mesh, where larger values lead to denser refinements. The density of vertices of faces_out is this factor times higher than the vertices of faces. 
faces_out
and vertices_out
is_triangle_mesh(tmesh)
#include <CGAL/Polygon_mesh_processing/refine.h>
void CGAL::Polygon_mesh_processing::split_long_edges  (  const EdgeRange &  edges, 
const double &  max_length,  
PolygonMesh &  pmesh,  
const NamedParameters &  np  
) 
splits the edges listed in edges
into subedges that are not longer than the given threshold max_length
.
Note this function is useful to split constrained edges before calling isotropic_remeshing()
with protection of constraints activated (to match the constrained edge length required by the remeshing algorithm to be guaranteed to terminate)
PolygonMesh  model of MutableFaceGraph that has an internal property map for CGAL::vertex_point_t . 
EdgeRange  range of boost::graph_traits<PolygonMesh>::edge_descriptor , model of Range . Its iterator type is InputIterator . 
NamedParameters  a sequence of Named Parameters 
pmesh  a polygon mesh 
edges  the range of edges to be split if they are longer than given threshold 
max_length  the edge length above which an edge from edges is split into to subedges 
np  optional Named Parameters described below 
vertex_point_map  the property map with the points associated to the vertices of pmesh . Instance of a class model of ReadWritePropertyMap . 
isotropic_remeshing()
#include <CGAL/Polygon_mesh_processing/remesh.h>
bool CGAL::Polygon_mesh_processing::triangulate_face  (  typename boost::graph_traits< PolygonMesh >::face_descriptor  f, 
PolygonMesh &  pmesh,  
const NamedParameters &  np  
) 
triangulates a single face of a polygon mesh.
This function depends on the package 2D Triangulation
PolygonMesh  a model of FaceListGraph and MutableFaceGraph 
NamedParameters  a sequence of Named Parameters 
f  face to be triangulated 
pmesh  the polygon mesh to which the face to be triangulated belongs 
np  optional sequence of Named Parameters among the ones listed below 
vertex_point_map  the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh 
geom_traits  a geometric traits class instance 
true
if the face has been triangulated. #include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
bool CGAL::Polygon_mesh_processing::triangulate_faces  (  FaceRange  face_range, 
PolygonMesh &  pmesh,  
const NamedParameters &  np  
) 
triangulates given faces of a polygon mesh.
This function depends on the package 2D Triangulation
FaceRange  range of boost::graph_traits<PolygonMesh>::face_descriptor , model of Range . Its iterator type is InputIterator . 
PolygonMesh  a model of FaceListGraph and MutableFaceGraph 
NamedParameters  a sequence of Named Parameters 
face_range  the range of faces to be triangulated 
pmesh  the polygon mesh to be triangulated 
np  optional sequence of Named Parameters among the ones listed below 
vertex_point_map  the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh 
geom_traits  a geometric traits class instance 
true
if all the faces have been triangulated. #include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
bool CGAL::Polygon_mesh_processing::triangulate_faces  (  PolygonMesh &  pmesh, 
const NamedParameters &  np  
) 
triangulates all faces of a polygon mesh.
This function depends on the package 2D Triangulation
PolygonMesh  a model of FaceListGraph and MutableFaceGraph 
NamedParameters  a sequence of Named Parameters 
pmesh  the polygon mesh to be triangulated 
np  optional sequence of Named Parameters among the ones listed below 
vertex_point_map  the property map with the points associated to the vertices of pmesh . If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh 
geom_traits  a geometric traits class instance 
true
if all the faces have been triangulated. #include <CGAL/Polygon_mesh_processing/triangulate_faces.h>